A multicomponent lattice Boltzmann scheme is used to investigate the surface coating of substrates with two topographical features by a gravity-driven thin liquid film. The considered topographies are $\mathsf{U}$- and $\mathsf{V}$-shaped grooves and mounds. For the case of substrates with two grooves, our results indicate that for each of the grooves there is a critical width such that if the groove width is larger than the critical width, the groove can be coated successfully. The critical width of each groove depends on the capillary number, the contact angle, the geometry, and the depth of that groove. The second groove critical width depends on, in addition, the geometry and the depth of the first groove; for two grooves with the same geometries and depths, it is at least equal to that of the first groove. If the second groove width lies between the critical widths, the second groove still can be coated successfully on the condition that the distance between the grooves is considered larger than a critical distance. For considered contact angles and capillary numbers our results indicate that the critical distance is a convex function of the capillary number and the contact angle. Our study also reveals similar results for the case of substrates with a mound and a groove.

• Received 28 August 2012

DOI:https://doi.org/10.1103/PhysRevE.87.022409